Construction of a complete set of orthogonal Fourier–Mellin moment invariants for pattern recognition applications

The completeness property of a set of invariant descriptors is of fundamental importance from the theoretical as well as the practical points of view. In this paper, we propose a general approach to construct a complete set of orthogonal Fourier–Mellin moment (OFMM) invariants. By establishing a relationship between the OFMMs of the original image and those of the image having the same shape but distinct orientation and scale, a complete set of scale and rotation invariants is derived. The efficiency and the robustness to noise of the method for recognition tasks are shown by comparing it with some existing methods on several data sets.